Question 1012691: Hi
box x box y box z contain marbles in the ratio of 5:7:3.If there are 56 more marbles in box y than box z, how many marbles in all 3 boxes
thanks
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20065)   (Show Source):
You can put this solution on YOUR website!
Use the principle:
If x:y:z = a:b:c
then
 ,  ,  .
We are given x:y:z = 5:7:3, then
 ,  , 
or
 ,  , 
Reducing and letting the sum x+y+z = s, the sum of the marbles
in the box,
 ,  , 
there are 56 more marbles in box y than box z
y = z+56
Cross multiply:
Solve by substitution. The answer is what you get for s.
Edwin
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! you are given that:
x:y:z = 5:7:3
y = z+56
y:z = 7:3 is the same as y/z = 7/3.
since y has 56 more marbles than z, then you get y = z+56.
replace y with z+56 in the formula of y/z = 7/3 to get (z+56)/z = 7/3
multiply both sides of the equation by z to get z+56 = 7z/3
multiply both sides of the equation by 3 to get 3*(z+56) = 7z
distribute the multiplication to get 3z + 168 = 7z
subtract 3z from both sides of the equation to get 168 = 4z
divide both sides of the equation by 4 to get z = 42
since y is 56 more than z, then y = 98
since the ratio of x:y = 5:7 is the same as x/y = 5/7, you get:
x/y = 5/7
since y = 98, the equation becomes x/98 = 5/7
multiply both sides of the equation by 98 to get x = 5 * 98/7
solve for x to get x = 70.
your solution is that x = 70, y = 98, and z = 42.
y is 56 more than z because 42 + 56 = 98.
ratio of x to y is 5/7 because 70/98 = 5/7.
ratio of y to z is 7/3 because 98/42 = 7/3.
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